Certified Impossibility Results for Byzantine-Tolerant Mobile Robots

TL;DR

This paper formalizes and proves impossibility results for Byzantine-tolerant mobile robots using the COQ proof assistant, establishing the first certified impossibility proofs in this domain.

Contribution

It introduces a formal framework in COQ for robot network properties and provides the first certified impossibility proofs for convergence under Byzantine failures.

Findings

Formal proofs of impossibility for >1/2 Byzantine robots

Formal proofs of impossibility for >1/3 Byzantine robots

Compact COQ developments for these proofs

Abstract

We propose a framework to build formal developments for robot networks using the COQ proof assistant, to state and to prove formally various properties. We focus in this paper on impossibility proofs, as it is natural to take advantage of the COQ higher order calculus to reason about algorithms as abstract objects. We present in particular formal proofs of two impossibility results forconvergence of oblivious mobile robots if respectively more than one half and more than one third of the robots exhibit Byzantine failures, starting from the original theorems by Bouzid et al.. Thanks to our formalization, the corresponding COQ developments are quite compact. To our knowledge, these are the first certified (in the sense of formally proved) impossibility results for robot networks.